{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T09:40:01Z","timestamp":1748598001564,"version":"3.41.0"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2015,8]]},"abstract":"<jats:p>The k-isoperimetric edge connectivity is a more refined network reliability index than edge connectivity. The k-isoperimetric edge connectivity of a connected graph G is defined as \u03b3<jats:sub>k<\/jats:sub>(G) = min{|[X, [Formula: see text]]| : X \u2286 V (G), |X| \u2265 k, |[Formula: see text]| \u2265 k}. Let \u03b2<jats:sub>k<\/jats:sub>(G) = min{|[X,[Formula: see text]]| : X \u2286 V (G), |X| = k}. A graph G is called a \u03b3<jats:sub>k<\/jats:sub>-optimal graph if \u03b3<jats:sub>k<\/jats:sub>(G) = \u03b2<jats:sub>k<\/jats:sub>(G). An edge cut S = [X,[Formula: see text]] is called a \u03b3<jats:sub>k<\/jats:sub>-cut if |S| = \u03b3<jats:sub>k<\/jats:sub>(G), X \u2286 V (G), |X| \u2265 k and |[Formula: see text]| \u2265 k. Moreover, G is called a super-\u03b3<jats:sub>k<\/jats:sub>graph if every \u03b3<jats:sub>k<\/jats:sub>-cut [X,[Formula: see text]] of G has the property that either |X| = k or |[Formula: see text]| = k. Let G be a graph of order at least 2k with k \u2265 2. In this paper, we prove that for any pair u, \u03c5 of nonadjacent vertices in G, if |N(u)\u2229N(\u03c5)| \u2265 k+1 when neither u nor \u03c5 lies on a triangle, or |N(u)\u2229N(\u03c5)| \u2265 2k -1 when u or \u03c5 lies on a triangle, then G is \u03b3<jats:sub>k<\/jats:sub>-optimal. Moreover, if G is a triangle-free graph, and |N(u)\u2229\u03c5(\u03c5)| \u2265 k +1 for all pairs u, \u03c5 of nonadjacent vertices in G, then G is either super-\u03b3<jats:sub>k<\/jats:sub>or isomorphic to K<jats:sub>k+1,k+1<\/jats:sub>.<\/jats:p>","DOI":"10.1142\/s012905411550032x","type":"journal-article","created":{"date-parts":[[2015,8,31]],"date-time":"2015-08-31T06:16:51Z","timestamp":1441001811000},"page":"583-598","source":"Crossref","is-referenced-by-count":0,"title":["Sufficient Conditions for Maximally k-Isoperimetric Edge Connectivity of Graphs"],"prefix":"10.1142","volume":"26","author":[{"given":"Shiying","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi, 030006, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yubao","family":"Guo","sequence":"additional","affiliation":[{"name":"Lehrstuhl C f\u00fcr Mathematik, RWTH Aachen University, 52056 Aachen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,8,30]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(99)90041-9"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)00369-T"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1137\/S089548019630635X"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.06.035"},{"issue":"6","key":"p_6","first-page":"858","volume":"36","author":"Wang Ming","year":"2002","journal-title":"Journal of Shanghai Jiaotong University"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1002\/net.20217"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.01.037"},{"issue":"1","key":"p_9","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1002\/net.20343","volume":"56","author":"Wang Shiying","year":"2010","journal-title":"Networks"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2006.06.028"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.08.066"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S012905411550032X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T09:18:58Z","timestamp":1748596738000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S012905411550032X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8]]},"references-count":10,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2015,8,30]]},"published-print":{"date-parts":[[2015,8]]}},"alternative-id":["10.1142\/S012905411550032X"],"URL":"https:\/\/doi.org\/10.1142\/s012905411550032x","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"type":"print","value":"0129-0541"},{"type":"electronic","value":"1793-6373"}],"subject":[],"published":{"date-parts":[[2015,8]]}}}